Trig sin and cos graphs n00b help.

[Dude22]

Homework Statement

Hi everyone. I understand the basics of trig graphing; but am having a hard time understanding f(x) first of all what to f and x stand for? Above and beyond that any help understanding f(x) or a link to a website that might help me would be great.

Homework Equations

f(x)...

The Attempt at a Solution

I have searched the web and cannot find an answer to my simple question.

I have watched videos on KHAN ACADEMY and understand almost everything about graphs but NOT f(x)

I have watched videos on YouTube

 

[lewando]

To start, it reads, "a function f of x". This means that "x" is an input to the function "f".
f(x), by itself is very general. f(x) can be specified by equating it to something like: f(x) =sin(x). f(x) can be considered an "output" where x is the "input".

Abide on that for awhile.

 

[collinsmark]

Hello Dude22,

Welcome to Physics Forums!

Homework Statement

Hi everyone. I understand the basics of trig graphing; but am having a hard time understanding f(x) first of all what to f and x stand for? Above and beyond that any help understanding f(x) or a link to a website that might help me would be great.

Homework Equations

f(x)...

The Attempt at a Solution

I have searched the web and cannot find an answer to my simple question.

I have watched videos on KHAN ACADEMY and understand almost everything about graphs but NOT f(x)

I have watched videos on YouTube

This question might be better off in the

Homework & Coursework Questions / Precalculus Mathematics​

subforum. But I suppose I can try to help out here.

Here 'f' means "function." It has an input and an output. The variable 'x' is the input. How do you know 'x' is the input? Because the function was denoted as "f(x)." If the input had nothing to do with 'x' but instead had 't' as the input, the function would be denoted as "f(t)."

When vocalizing, "f(x)" is pronounced: f of x.

Not all functions have to be named 'f' though. They could be named 'g', or anything. So g(x) can also be a function of x, and is pronounced g of x.

Maybe I should show an example. Consider the following function:
$$x^2$$
If x is 1, the function output is 1.
If x is 2, the function output is 4.
If x is 3, the function output is 9.
The input of the function is 'x', and we can name the function 'f'. So we can say,
$$f(x) \equiv x^2$$
Note that this is sort of similar to the notation $y = x^2$. So why don't we just use that? Because we're not intending to set the function equal to something and make an equation; rather we are essentially naming the function.

Lastly, be aware of the ambiguity with the multiplication notation. f(x) is not the same thing as f times x, or (f)(x). That's something totally different. But the notation is similar if not identical. You'll have to figure out the meaning from the context.

Here is a Wikipedia article on functions. It goes from basic to pretty advanced quickly. But for what it's worth,
http://en.wikipedia.org/wiki/Function_%28mathematics%29

Good luck!